I suspect most of these "They could shoot ours" stories are either urban legends or Old Wives Tales if you prefer, what interchangeability of ammunition between different countries rifles-unless they were using Mausers-were purely coincidental. Regarding the British selecting the 9MMP for the Sten Gun, their.380 revolver cartridge was unsuitable for SMG use, and any 9MM ammunition captured from the Italians would have been 9MM Glisenti, probably too weak for SMG use. Plus it would have stayed in North Africa-shipping was pretty tight then.
In the Cuban Campaign the Rough Riders had 2 Colt M1895 "potato diggers" chambered in 7MM Mauser-does that count?